Astronomical hydrodynamics is usually almost ideal in the sense that the Reynolds number (Re) is enormous and any effective viscosity must be due to shocks or turbulence. Astronomical magnetohydrodynamics (MHD) is often also nearly ideal, so that magnetic fields and plasma are well coupled. In particular, dissipation of orbital energy in accretion disks around black holes is readily explained by MHD turbulence. On the other hand, the planet-bearing disks around protostars are magnetically far from ideal because of very low fractional ionization. MHD turbulenc

We review recent breakthroughs in understanding
some general features of the Renormalization Group and of Quantum Field Theory.
We discuss some applications of these new results and their deep connection to
the entanglement of the Quantum Field Theory vacuum.

There is strong theoretical evidence that black holes have a finite thermodynamic entropy equal to one quarter the area A of the horizon. Providing a microscopic derivation of the entropy of the horizon is a major task for a candidate theory of quantum gravity. Loop quantum gravity has been shown to provide a geometric explanation of the finiteness of the entropy and of the proportionality to the area of the horizon. The microstates are quantum geometries of the horizon.

Shape Dynamics first arose as a theory of particle interactions formulated without any of Newton's absolute structures. Its fundamental arena is shape space, which is obtained by quotienting Newton's kinematic framework with respect to translations, rotations and dilatations. This leads to a universe defined purely intrinsically in relational terms. It is then postulated that a dynamical history is determined by the specification in shape space of an initial shape and an associated rate of change of shape.

Majorana disappeared under mysterious circumstances in 1938 and the particle that bears his name remains elusive to experiments. There is growing interests in realizing the Majorana bound state in the Laboratory because it is expected to possess unusual properties such as non-abelian statistics. I shall discuss various proposals to produce Majorana bound states and the associated topological superconductors which support them.

There has been some significant recent progress on the long-standing problem of identifying the conditions under which equilibrium statistical mechanics can arise from an exact quantum mechanical treatment of the dynamics. I will give an overview of this progress, describing in particular how random matrix models and the associated concentration of measure phenomena imply that equilibration is generic even for the closed system evolution of pure quantum states.